LESSON
9.5
Solving Volume
Problems
ESSENTIAL QUESTION
7.G.2.6
Solve real-world and
mathematical problems
involving … volume of …
three-dimensional objects
composed of … cubes, and
right prisms.
How do you find the volume of a figure made of cubes
and prisms?
Volume of a Triangular Prism
The formula for the volume of a rectangular prism can be used for any prism.
Volume of a Prism
The volume V of a prism is the area of its base B times its height h.
V = Bh
EXAMPLE 1
7.G.2.6
Bradley’s tent is in the shape of a triangular prism.
How many cubic feet of space are in his tent?
STEP 1
Find the base area B of the triangular prism.
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Area of a triangle with base length b and height h
Substitute 6 for b and 4 for h.
STEP 2
Find the volume of the prism.
Volume of a prism with base area B and height h
Substitute 12 for B and 9 for h.
The volume of Bradley’s tent is 108 ft3 .
Reflect
1. Analyze Relationships For a prism that is not a rectangular prism,
how do you determine which sides are the bases?
YOUR TURN
2. Find the volume of the prism.
Lesson 9.5
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289
Volume of a Trapezoidal Prism
Prisms are named for the polygons that form their bases. In this lesson, you will
focus on prisms whose bases are either triangles or quadrilaterals other than
squares and rectangles.
EXAMPLE 2
7.G.2.6
Cherise is setting up her tent. Her tent is in the shape of a
trapezoidal prism. How many cubic feet of space are in her
tent?
STEP 1
Find the base area B of the trapezoidal prism.
Area of a trapezoid with bases of lengths b1 and b2
and height h
Without calculating the
volumes, how can you
know whether Bradley’s
or Cherise’s tent has a
greater volume?
Substitute 6 for b1 , 4 for b2 , and 4 for h.
STEP 2
Find the volume of the prism.
Volume of a prism with base area B and height h
Substitute 20 for B and 9 for h.
The volume of Cherise’s tent is 180 ft 3 .
Reflect
4. What If? How would doubling all the dimensions of the prism affect
the volume of the tent?
YOUR TURN
5. Find the volume of the prism.
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Unit 4
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3. Look for a Pattern How could you double the volume of the tent by
doubling just one of its dimensions?
Volume of a Composite Solid
You can use the formula for the volume of a prism to find the volume of
a composite figure that is made up of prisms.
EXAMPLE 3
7.G.2.6
Allie has two aquariums connected by
a small square prism. Find the volume
of the double aquarium.
STEP 1
My Notes
Find the volume of each
of the larger aquariums.
Volume of a prism
Substitute 3 × 4 = 12 for B and 3 for h.
STEP 2
Find the volume of the connecting prism.
Volume of a prism
Substitute 1 × 1= 1 for B and 2 for h.
STEP 3
Add the volumes of the three parts of the aquarium.
V = 36 + 36 + 2 = 74 ft3
The volume of the aquarium is 74 ft3.
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Reflect
6. What If? Find the volume of one of the large aquariums on either end
using another pair of opposite sides as the bases. Do you still get the
same volume? Explain.
YOUR TURN
7. The figure is composed of a rectangular
prism and a triangular prism. Find the
volume of the figure.
Lesson 9.5
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291
Guided Practice
1. Find the volume of the triangular prism. (Example 1)
2. Find the volume of the trapezoidal prism. (Example 2)
3. Find the volume of the composite figure. (Example 3)
Volume of rectangular prism =
Volume of triangular prism =
Volume of composite figure =
Find the volume of each figure. (Examples 2 and 3)
5. The figure shows a container, in the shape of
a trapezoidal prism, that Pete filled with sand.
ESSENTIAL QUESTION CHECK-IN
6. How do you find the volume of a composite solid formed by two
or more prisms?
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4. The figure shows a barn that Mr. Fowler is
building for his farm.